Hudson (12-4) allowed two hits and one walk in 6 2-3 innings and won his sixth straight decision.
After being held to five hits in a 4-1 loss to the Padres on Monday, the Braves had 10 hits, including Dan Uggla's 14th homer.
The Braves began the day 5 1/2 games behind first-place Washington in the NL East, their biggest deficit since trailing by 6 games on July 5, but they gained a game back on the Nationals to cut the deficit to 4 1-2 games.
Jonny Venters, Luis Avilan and Craig Kimbrel completed the shutout.
Clayton Richard (9-12) left the game trailing 3-0, after giving up two hits in the seventh. Prado homered off Brad Boxberger to make it 6-0.
Richard allowed five runs and nine hits in 6 1-3 innings for the Padres, who lost for the third time in 11 games.
GIANTS 6, NATIONALS 1
SAN FRANCISCO (AP) — Madison Bumgarner pitched a five-hitter, and Brandon Belt had three hits and three RBIs, leading San Francisco over Washington in a matchup of NL division leaders.
Bumgarner (13-7) struck out six and walked one in his second complete game this season.
Hunter Pence and Marco Scutaro both added three hits for the Giants, who have won three of four at home after losing eight of nine.
Pablo Sandoval, in his first start since coming off the disabled list on Monday, Angel Pagan and Brandon Crawford also drove in runs.
Adam LaRoche knocked in the lone run for the Nationals, who have won 11 of 14.
NL ERA leader Jordan Zimmermann (9-7) had a six-game winning streak end after he allowed two runs and eight hits. Zimmermann has allowed four earned runs or fewer in his 24 starts this season, and two or fewer in 18.
REDS 3, METS 0
CINCINNATI (AP) — Jay Bruce hit a three-run homer in the ninth inning, and Cincinnati won its fourth game in a row, beating the New York Mets.
The NL Central leaders and the Mets were a combined 0 for 18 with runners in scoring position before Bruce connected with no outs.
Brandon Phillips drew a leadoff walk in the ninth from Manny Acosta (1-3), New York's fifth pitcher. Ryan Ludwick followed with single that sent Phillips to second.
Left-handed reliever Josh Edgin came in to face the lefty-hitting Bruce, who sent a drive into the left-field seats. It was Bruce's 23rd homer of the season and second in the Reds' last two games — both off lefties.
Jose Arredondo (5-2) wound up with the win. In all, the clubs stranded a total of 24 runners on base.
DODGERS 11, PIRATES 0
PITTSBURGH (AP) — Chad Billingsley pitched eight dominant innings, and Los Angeles matched its highest-scoring game of the season, routing Pittsburgh.
The Dodgers have won five of six, pushing them to the top of the NL West. Pittsburgh has lost five of six.
Luis Cruz tied career highs for hits and RBIs with three each. Hanley Ramirez added three hits, two RBIs and two runs as Los Angeles beat the Pirates for the eighth straight time, dating to last season.
Billingsley (9-9) won his fifth consecutive start, allowing five hits and one walk. He improved to 7-1 in his career against the Pirates.
Kevin Correia (9-7) had won seven straight decisions, tied for the longest active streak in the majors.
Shawn Tolleson worked a perfect ninth to preserve the Dodgers' seventh shutout of the season. The Pirates have been blanked 10 times.
PHILLIES 1, MARLINS 0
MIAMI (AP) — Kyle Kendrick pitched five-hit ball for seven innings, and Jimmy Rollins homered off Josh Johnson to start the game, leading Philadelphia past Miami.
Charlie Manuel earned his 700th win as a manager with the Phillies' second straight shutout. Cole Hamels opened the series between NL East rivals with a 4-0 victory.
The Marlins haven't scored in 27 innings.
Kendrick (5-9) struck out six and threw 61 of 87 pitches for strikes. He has won seven straight against the Marlins, dating to September 2008.
Josh Lindblom and Jonathan Papelbon each pitched a hitless inning. Papelbon walked Carlos Lee with two outs and then got Giancarlo Stanton to ground out for his 26th save.
Johnson (7-9) went eight innings and allowed three hits. He struck out seven and walked one.
ASTROS 10, CUBS 1
CHICAGO (AP) — Brett Wallace and Fernando Martinez each hit three-run homers to back Lucas Harrell's eight strong innings, and Houston routed the Chicago Cubs.
Harrell (10-8) scattered six hits and struck out six, helping the Astros win for only the third time in 28 road games. Harrell has allowed two runs or fewer in all seven of his starts since the All-Star break.
Scott Moore added a solo shot and doubled twice for a career-high three extra-base hits. Jose Altuve also doubled twice and had three of Houston's 13 hits.
Chris Volstad (0-9) lasted just five innings, allowing eight hits and four runs in his latest bid for his first big league win since July 10, 2011. He hasn't won in 23 starts and is approaching the major league record of 28.
Volstad is 0-14 with a 5.51 ERA during his skid.
The Cubs, who have lost 12 of 14, matched their season high by falling 25 games under .500, their worst record since finishing the 2006 season 30 games below.
CARDINALS 8, DIAMONDBACKS 2
ST. LOUIS (AP) — Rookie Joe Kelly pitched into the seventh inning of what could be his final start before Jaime Garcia comes off the disabled list, and St. Louis got home runs from Matt Holliday and Jon Jay in a victory over Arizona.
Miguel Montero hit a two-run homer for the Diamondbacks (58-58), who have lost four of six. They are 0-4 against the Cardinals.
Ian Kennedy (10-10) made throwing errors on consecutive plays to help the Cardinals score two unearned runs in the seventh for a three-run cushion, and gave up both homers for a four-game total of eight.
Kelly (3-5) gave up two runs in 6 1-3 innings and matched his career best with six strikeouts, lowering his ERA to 3.41 — trailing only Kyle Lohse's 2.72 in the rotation.
ROCKIES 8, BREWERS 6
DENVER (AP) — Carlos Gonzalez had four hits, Tyler Chatwood pitched six effective innings and Colorado beat Milwaukee.
Eric Young Jr. homered among his three hits, and Wilin Rosario also connected for Colorado, which had 15 hits for the second straight night.
Rafael Betancourt finished up a shaky ninth to record his 21st save.
Martin Maldonado homered, and Norichika Aoki had three hits for the Brewers, who had another late rally fall short.
Chatwood (3-2), coming off five shutout innings in San Francisco, had another strong outing. He allowed two runs — one earned — on four hits and struck out three.
The Rockies kept pounding Milwaukee pitchers. On Monday, they jumped in front early and they repeated the formula against Randy Wolf (3-9).